Use the following to answer the question(s) below.
A government agency has 6000 employees. As an alternative to the traditional five day work week, employees were asked whether they preferred a four-day work week (10 hours per day) or flexible hours. The table below shows the results by age category.

-Two events F = {a randomly selected employee prefers flex hours} and O = {a randomly selected employee is over 45 years old} are
A) independent.
B) mutually exclusive.
C) not independent.
D) independent and mutually exclusive.
E) disjoint.

Question

Use the following to answer the question(s) below.
A government agency has 6000 employees. As an alternative to the traditional five day work week, employees were asked whether they preferred a four-day work week (10 hours per day) or flexible hours. The table below shows the results by age category.
 
-Two events F = {a randomly selected employee prefers flex hours} and O = {a randomly selected employee is over 45 years old} are
A) independent. 
B) mutually exclusive. 
C) not independent. 
D) independent and mutually exclusive. 
E) disjoint.

Quizplus · Accepted Answer

The events F and O are not independent because knowing the age category of an employee affects the probability of them preferring flexible hours. For example, the probability that an employee over 45 years old prefers flexible hours is 0.53, while the probability that an employee under 45 years old prefers flexible hours is only 0.37. Therefore, the two events are dependent on each other.

Use the Following to Answer the Question(s) Below